How would the reverse switch cause the car to die? Its only purpose is to keep the car from cranking if not in neutral and to complete the circuit for the reverse lights. It has nothing to do with the actual ignition so once its running I dont see how it can cause the car to cut off.
Y a know what this is the most brilliant post Ive seen in a while and Im not being a smart azz...:) I agree 100% I was going to guess the reverse band then say tweak the idle up a bit...